Heterogeneity in Neuronal Calcium Spike Trains based on Empirical Distance

Statistical similarities between neuronal spike trains could reveal significant information on complex underlying processing. In general, the similarity between synchronous spike trains is somewhat easy to identify. However, the similar patterns also potentially appear in an asynchronous manner. However, existing methods for their identification tend to converge slowly, and cannot be applied to short sequences. In response, we propose Hellinger distance measure based on empirical probabilities, which we show to be as accurate as existing techniques, yet faster to converge for synthetic as well as experimental spike trains. Further, we cluster pairs of neuronal spike trains based on statistical similarities and found two non-overlapping classes, which could indicate functional similarities in neurons. Significantly, our technique detected functional heterogeneity in pairs of neuronal responses with the same performance as existing techniques, while exhibiting faster convergence. We expect the proposed method to facilitate large-scale studies of functional clustering, especially involving short sequences, which would in turn identify signatures of various diseases in terms of clustering patterns.

I. Introduction

Neurons encode stimulus information in spike trains. In fact, heterogeneity in spike trains is a known manifestation of complex information processing, which enables diverse functions in the hippocampus, a brain region associated with memory and learning [1]. The said heterogeneity in spike trains has been investigated by clustering neuron pairs based on certain statistical similarities. An early attempt in this direction was based on a correlation-based similarity measure [2]. However, such a measure captures coincident firing, i.e., synchronicity in spike trains, but ignores time-delayed versions of similar patterns which are known to arise in complex neuronal networks. As a remedy, distance measures based on Lempel-Ziv (LZ) encoding have been suggested to identify the statistical similarities in synchronous or asynchronous spike trains [3], [4]. One such method was based on LZ-78 algorithm which needs long sequences for reliable performance. In the quest for a method that can be applied to short sequences, we consider LZ-76, a LZ-based fast method, but find it to be inaccurate. Against this backdrop, we propose a Hellinger distance measure based on empirical probabilities of patterns in each pair of spike trains [5]. Our method converges faster than LZ-78, and hence may be used on short sequences, while being comparably accurate. Further, we cluster pairs of neuronal spike trains and found two non-overlapping classes, and the clusters obtained using the proposed distance measure and the distance based on LZ-78 are found to behave similarly. This demonstrates the suitability of the proposed method as a fast-converging alternative to the existing slow technique. Fig. 1.

Intracellular calcium imaging: representative image of hippocampal neuron population with 28 neurons. Scale bar = 20 µm [5].

Fig. 2.

Schematic workflow.